Problem: Solve for $x$ and $y$ using elimination. ${-2x+y = -9}$ ${-5x-y = -40}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-7x = -49$ $\dfrac{-7x}{{-7}} = \dfrac{-49}{{-7}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-2x+y = -9}\thinspace$ to find $y$ ${-2}{(7)}{ + y = -9}$ $-14+y = -9$ $-14{+14} + y = -9{+14}$ ${y = 5}$ You can also plug ${x = 7}$ into $\thinspace {-5x-y = -40}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ - y = -40}$ ${y = 5}$